The star M.D. from "Botched" commissioned Harakh Mehta of Harakh Jewelers to get the ball rolling ... first with a massive engagement ring that cost Nassif around $165k. Mehta tells us the engagement ring -- pure platinum, BTW -- is practically an iceberg ... 3.15-carat center stone stealing the show (behind Brittany, of course).

We're told the jeweler also created not one but 2 wedding bands for Brittany -- 2 full eternity diamond bands totaling 1.24 carats crafted in pure platinum. Price tag -- around $9k.

So, why 2 wedding bands? Mehta says, "We specially crafted two bands rather than one to surround the engagement ring which marked the two milestones in their life."

Mehta tells us it took around 4 months to make the rings. The doc proposed to Brittany back in June and they tied the knot in L.A. followed by a reception in Santorini, Greece earlier this month.

BTW ... Nassif sang to Brittany at their wedding. And, no ... he didn't botch it!!!